How do I make an object partially transparent in the 3D view?
In the bottom right area of your top photo, there are 2 settings visible: Blend Mode and Shadow mode, both are defaulted to opaque. Set Blend Mode to alpha-hashed, alpha-clip, or alpha blend. The other controls shadows cast by the transparency - you may or may not need it. You still can control the degree of transparency using the alpha value.

Alternatively, you could always enable x-ray mode at the top next to the viewport preview selection buttons.